You need to make a better distinction between "paragraphs" and lines of text.
A paragraph style is applied to an entire paragraph, and a paragraph is everything from one hard return to another. Only a hard return will split a paragraph. Your sample doesn't show it, but it bears all the hallmarks of having soft line breaks (shift+enter) instead of hard returns at the end of each line.
So either make each line a "paragraph", or don't use paragraph styles at all. If all you need is to make some text bold, you might as well use a character style -- or (getting into the Advanced Stuff now) use a Line Style to make each first line bold.
First, please ALWAYS include the version of ID and the OS when posing a question. Features are different from verion to version and OSs behave differently. I checked your other thread, and I believe you are using CS5.5, but it owould be fater to have all that up front.
Paragraph styles provide the basic formatting for a paragraph, hence the name. If you want something other than the basic style for particular text within any given paragraph you apply a a Character style. This can be done manually to a local selection, or through automated techniques of Nested Styles, Line Styles or GREP Styles when there is a pattern that can be used to trigger the character style application. In your example I see three possibilities:
1) Use two (or more) different paragraph styles, and make the first line a paragraph all by itself. In the example it appears that it really is a separate entity spaced apart from the rest of the text. In fact each line could be a separate paragraph in poetry, and if you have the smae number of lines in each stanza you can use a separate style for each line, then set the "Next Style" property to rotate through automatically, with the last style having its "next style" set to the style for the first line of the next stanza. Lines that "look" like they have the same formatting can use "based on" styles, changing only the "next style" field.
2) Use a nested style tiggered by a forced line break. This is the "old" method and is still valid when the material you want to format differntly might break across two or more lines, i.e. your first line that you want bold might be too long for the width of your column and you want all of it bold, not just the part on the very first line.
3) Use a Line Style, which applies the character style to the decginated number of lines, regardless of wheter that encompasses a full sentence, part of a sentence, or a full sentence plus a fragment.
Note that options 2 and 3 require you to create a character style to be applied (which you can do from the paragraph style dialog in CS5.5). Best practice is to make that style definition do as little as possible, i.e. if all you want is to make the text bold or italic, that is the only property you should set, leaving the font family blank, and the style will then work with any font that has a bold or italic (respectively) variant, and changing the base font in the paragraph style won't leave you with text inthe wrong font where your nested or line styles are applied. Option 1 requires full specifications for all styles, but using Based On attributes you can change only those things, like the font weight or style, and the "next style" that should be different, and any subsequent changes made to the base style will cascade through all the based on styles except where the change would be in conflict.